Use of Curve Modifier to Make G2 Timing Belt
Thanks to @moonboots for the comment pointing me in the right direction.
The answer was to go into edit mode for the curve, select all the points, and then set the &quot;Mean Radius&quot; for all of the points in the curve to 1.
If you &quot;apply&quot; a scale to a curve object, the radius of all the points is subsequently changed from its previous value to a scaled version of the radius.  Blender is simply &quot;applying&quot; the scaling factor you have selected to some of the internal properties.  For example, if you scale your curve by 0.5, then the radius for each point is then changed to 0.5 times its original value.  Typically, the radius is set to 1 (unless you are doing something interesting and fun).  Then when Blender uses the curve in a curve modifier, it will scale the original object by the values in the radius as it is placed along the curve.  This is why setting the radius back to 1 (i.e. no scaling) fixes this problem.